Yes, this hypothesis is probably medically implausible. I am postulating it to examine the principles involved. Please accept it for that purpose.
Suppose a medical treatment is developed which is safe, effective and inexpensive. It halts the aging process permanently. However, after twelve decades of life, the mind of the person “collapses” and the person becomes brain dead, like Karen Ann Quinlan. They can be maintained in this state indefinitely, even for centuries, with nasogastric feeding.
What is the moral thing to do with such people?

I know this is not in your eschatology, but if, millennia from now, there were human colonies many light years away, would they need their own Popes because of the taking of decades to communicate with Earth?

Licit Churches in the East operate as their own entity, in communion with Rome, but with a leader called a pope or patriarch. But in your hypothetical, there could still be only one Roman Pontiff with the authority of Saint Peter.